Question

1. geometry write and solve an equation to find the value of x so that the figures have the same area.

Explanation:

Step1: Calculate area of first rectangle

Area = (5 + x) * 9 = 9(5 + x)

Step2: Calculate area of second rectangle

Convert \(15\frac{3}{7}\) to improper fraction: \(\frac{108}{7}\). Area = \(x \cdot \frac{108}{7}\)

Step3: Set areas equal and solve for x

\(9(5 + x) = \frac{108}{7}x\)
Expand left: \(45 + 9x = \frac{108}{7}x\)
Subtract \(9x\) (=\(\frac{63}{7}x\)): \(45 = \frac{45}{7}x\)
Solve for x: \(x = 7\)

Answer:

7